CORRECTION: The original version of this article was accompanied by a photograph of the Princeton Plasma Physics Laboratory. The photograph has been taken down because the person appearing in the photo was not one of the employees who received the payments in question.

Four high-ranking federal lab workers found a way to turn “per diem” funds for a temporary assignment into a steady flow of extra income — at taxpayers’ expense. The overpayments, discovered in an inspector general’s audit, boosted the annual pay of some of the employees by as much as $64,000.

The Department of Energy paid the four scientists roughly $1.8 million for daily lodging and “inconvenience” during assignments away from home. But these scientists were paid as if they were on temporary duty for up to 14 years — long after most had permanently relocated to job sites.

Princeton University, which the Energy Department pays to run its federal lab for fusion and plasma research, used taxpayer dollars to fund “per diem” payments for the employees’ lodging, as well as “premium” bonuses to supplement their salaries by an additional 12 percent. The extra money — which the university said was reviewed and approved by the Energy Department — was supposed to make up for the expense and difficulty of traveling to an assignment far from home.

Two of the Princeton lab employees worked on what the department considered a “temporary” travel detail for a scientific partnership at a General Atomics research facility in San Diego — one for 14 years and another for nine years. But both had long ago moved to the San Diego area.

Still, taxpayers spent more than $1 million in per diem payments to subsidize the living expenses of the two workers because their details were approved year after year. Taxpayers also provided the pair with $372,000 in “field service premiums,” a kind of bonus to compensate for the disruption caused by temporary, out-of-town duty. The office of Inspector General Gregory H. Friedman, the Energy Department’s watchdog, discovered the payments for the two workers last month and called them “unreasonable” and “questionable costs” in its public report, which was released late Friday.

When Friedman’s office alerted the department to the payments in April, top agency managers reviewed the books for the Princeton Plasma Physics Laboratory, one of 10 scientific research laboratories that private contractors run at government expense. The Princeton lab’s annual budget is $80 million, which is provided by the Energy Department. The department then discovered two additional federally paid lab employees who were overpaid based on the same mistakes.

One had received $400,000 in per diem and bonus payments after being classified as “on travel,” beginning in 2002, to work at the Massachusetts Institute of Technology in Cambridge. Another had been on “extended travel” to the Oak Ridge National Laboratory in Tennessee since 2007 and had been paid $95,000 in lodging reimbursements, according to information provided by a person briefed on the case, who spoke on the condition of anonymity to discuss a pending investigation.

The department immediately cut off the payments to the four employees.

Princeton University has agreed to reimburse the Energy Department $1 million for part of the costs. University Vice President and Secretary Bob Durkee said the lab began the temporary assignments with good intentions — to encourage scientific collaboration among the lab and other leading fusion research centers. Durkee said the Energy Department annually approved extending temporary assignments that worked well and payments that were allowed under the policy.

“We’ve agreed to reimburse some of the dollars and focus on the science going forward — not because we did anything wrong, but because we understand people think the reimbursements didn’t need to be so high,” Durkee said in an interview Friday.

The Energy Department called Princeton’s repayment “an offer of good faith and in recognition of its stewardship of taxpayer funds” but suggested that the payments were a surprise to its headquarters. In a letter responding to the report, the agency told Friedman that it “wholeheartedly agrees with the Inspector General’s recommendations.” The department said that it took “swift action” to stop the excessive payments when it was alerted of them and that it blamed a 1998 Princeton lab policy that allowed temporary assignments to continue for as long as three years — and to be extended.

“We have verified that no other laboratories have similar extended arrangements in place beyond three years, and we have replaced the 1998 policy with a strong, new department-wide policy that prevents reimbursements for extended assignments beyond three years and requires rigorous review of those assignments to ensure that taxpayers are getting the value they are expecting,” Dan Leistikow, an Energy Department spokesman, said Friday.

The new policy will also end the salary supplement for out-of-town travel.

The inspector general report does not name the four employees, who still are contractors for the department.

In the agency’s response to Friedman, it elaborated on its deeper look at how the travel payments got by and its conclusion that none of the other nine contractor-run science labs had such problems.

“Consistent with your recommendation, the Office of Management is issuing guidance to our contractors setting clear guidelines and requirements on compensation and reimbursements during extended assignments,” wrote Ingrid Kolb, the director of the office. “Finally, we are reviewing the actions and decisions by federal employees responsible for review of the travel costs here, and we will review our internal processes to ensure that excessive travel costs are not reimbursed going forward.”

The inspector general’s auditors found several factors that contributed to the payment errors.

“Neither Princeton nor the Department’s Princeton Site Office had taken what we would consider to be appropriate action to protect taxpayer interests by controlling the costs of these extended assignments,” the inspector general’s report said.

The report said that each of the employees’ formal contracts stated they were on one- or two-year assignments, but that “Princeton had extended the agreements annually without documenting the reasons for continuing the assignments or considering alternatives.”

The lab’s goal is to harness nuclear fusion as an energy source, a costly endeavor that requires experiments in which temperatures can reach as high as 30 million degrees — hotter than the sun. The lab carries out experiments in devices that confine plasma — a hot, electrically charged gas — by using magnetic fields inside a vacuum chamber.

The lab has undergone significant transition. It phased out construction of its National Compact Stellarator Experiment and instead began focusing on its flagship work, the National Spherical Torus Experiment. The university has managed the lab since its inception in 1951 and won another long-term contract last year.